Moment of a couple: resultant couple

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William Haynes

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Question statement

{applet}

Two couples act on a rectangle with a base of $\var{B}$ and a height of $\var{H}$ .

Determine the magnitude and direction of the resultant moment, knowing that $F = \var{F}$ and $G = \var{G}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

base	integer	7
height	integer	9
alpha	integer	100
units	list	[ "lb", "in" ]
G	quantity	quantity(50, "lbs")
b	quantity	quantity(7, "in")
h	quantity	quantity(9, "in")
F	quantity	quantity(65, "lbs")
dperp	quantity	quantity(5.330820672083086, "in")
M_f	quantity	quantity(346.50334368540059, "lbs*in")
M_g	quantity	quantity(-450, "lbs*in")
M_t	quantity	quantity(-103.49665631459941, "lbs*in")
applet	ggbapplet	HTML node
params	dict	Dictionary with 2 entries

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Value

xxxxxxxxxx
 
random(2..10)

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Description

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Generated value: `integer`

→ Used by:

b
params

Parts

Gap-fill
1. Gap mag Engineering Accuracy with units
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2. Gap dir Choose one from a list
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Gap-fill

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The resultant moment has a magnitude of mag in the dir direction. {M_t}

Advice

Let h be the height of the rectangle and $d_\perp$ be the perpendicular distance between the lines of action of F and F'.

Use the geometry of the problem to determine $d_\perp = \var{display(abs(dperp))}$

$M_F = F \cdot d_\perp = (\var{f}) (\var{display(abs(dperp))}) = \var{display(abs(M_f))}$ {if(sign(M_F)=1,'Counterclockwise','Clockwise')}

$M_G = G \cdot h =$ ({g}) ({h}) = {display(abs(M_g))} Clockwise

$M_T = \Sigma M = M_F + M_G = (\var{display(M_F)}) + (\var{display(M_G)}) = \var{display(M_t)}$

$M_T = \var{display(abs(M_T))}$ {if(sign(M_T)=1,'Counterclockwise','Clockwise')}

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Taxonomy: mathcentre

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William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

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Moment of a couple: resultant couple

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`